Question

A sharp stone of 2kg mass falls from a height of 10m on sand and buries into sand .It comes ti rest in a time of 0.029 second. The depth through which it buries into sand is

Answer 1

A sharp stone of 2kg mass falls from a height of 10m on a sand and buries into sand. it comes to rest in a time of 0.029 sec.

To find : The depth through which it buries into sand is ...

solution : mass of sharp stone, m = 2kg

height of stone from the surface of the sand, h = 10m.

initial velocity of sharp stone, u = 0

using formula, v² = u² + 2as

here, u = 0, a = 9.8 m/s², s = 10 m

so, v² = 0 + 2 × 9.8 × 10 = 196

v = 14 m/s

let stone buries s distance into the sand.

using formula, v = u + at

here v = 0, u = 14 m/s and t = 0.029

so, 0 = 14 + 0.029a

⇒a = -14 × 1000/29 = -482.76 m/s²

now using formula, v² = u² + 2as

here v = 0, u = 14 m/s and a = -482.76 m/s²

so, 0 = (14)² + 2 × (-482.76) s

⇒s = 14²/2(482.76) = 0.2m

Therefore the depth through which it buries into the sand is 0.2 m